FOUNDATION X DPP : 1 MATHEMATICS Chapter 1: Number system Old ICC building, near Firoz Hospital, Sir Syed N agar, Medical Road , Aligarh : 9997607607, 9997394458 1. The collection of real numbers and imaginary numbers is known as : (a) Rational no (b) Irrational no (c) Complex no (d) None of these 2. A complex no consists of a real part and a/an : (a) Rational part (b) Irrational part (c) Imaginary part (d) None of these 3. For a complex no, z x iy, to be purely real : (a) Real part of 0 z (b) I maginary part of 0 z (c) Real and imaginary part both should be zero (d) Complex no, 0 z 4. 0 is a : (a) purely real complex no (b) purely imaginary complex no (c) purely real as well as purely imaginary complex no (d) Not a complex no 5. The real part in a complex no, 5 5 z (a) 5 (b) 5 (c) 1 (d) – 1 6. The imaginary part in a complex no, 9 16 z is (a) 4 i (b) 4 i (c) 4 (d) – 4 7. 2 3 4 i i i i ? , where 1 i (a) – 1 (b) 1 (c) 0 (d) Not defined 8. 7 i is equal to (where 1 i ) (a) i (b) i (c) 1 (d) – 1 9. The number which can’t be represented on number line is (a) 2.5 (b) 1 3 (c) 3 (d) 5 10. 4 9 ? (a) – 6 (b) 6 i (c) 6 (d) 6 i 11. Represent 4 16 in a ib form (a) 0 (b) 8 (c) 4 4 i (d) 4 4 i 12. The complex conjugate of 3 3 is (a) 3 3 (b) 3 3 (c) 3 3 (d) 3 3 13. The product of 3 4 z i and its complex conjugate is (a) 16 (b) – 16 (c) 25 (d) – 7 Daily Practice Problems: 1 ( Basics of Complex Number ) FOUNDATION X DPP : 1 MATHEMATICS Chapter 1: Number system Old ICC building, near Firoz Hospital, Sir Syed N agar, Medical Road , Aligarh : 9997607607, 9997394458 14. 3 1 2 8 i i i ? (a) 1 256 i (b) 1 256 (c) 1 256 i (d) 3 1 256 i 15. 3 5 3 i can be expressed in a ib form as (a) 10 198 i (b) 10 198 i (c) 10 198 i (d) 10 198 i 16. The value of i 457 is (a) 1 (b) – 1 (c) i (d) – i 17. The standard form of 1 1 3 1 i i i is – (a) i 3 (b) i 3 (c) 3 1 i (d) 3 1 i 18. If ( x + i y ) (2 – 3i) = 4 + i , then real values of x and y are – (a) 14 , 5 y x (b) 13 14 , 5 13 y x (c) 13 14 , 13 5 y x (d) None of these 19. The conjugate of i 5 3 1 is – (a) ) 5 3 ( 34 1 i (b) 3 + 5i (c) i 5 3 1 (d) i 5 3 34 20. If , i c i c ib a where c is real, then a 2 + b 2 = (a) i (b) 1 (c) – 1 (d) 0 ANSWER KEY 1. c 2. c 3. b 4. c 5. b 6. d 7. c 8. b 9. d 10. b 11. c 12. d 13. c 14. a 15. b 16. c 17. a 18. c 19. a 20. b